The problem with municipal yard waste is you won't know what they put on it. If there are hard to kill weed seeds or if homeowners used long acting herbicides, the mulch would have to be composted first. If there might have been herbicides used then the compost needs to be aged for at least a year or you can do a test grow with cucumber seeds when the compost is mature to see if any herbicide damage shows up.
You might be able to get free mulch from local tree trimmers. You will have to inspect it first to make sure it was just tree trimmings and no roots or weeds. No palms or walnut trees. You can add that to a compost pile or use it as mulch for the garden. You cannot use mulch as compost. As it decomposes it steals nitrogen.
If you have dairy, chicken farms or stables nearby you might be able to get manure for free or low cost. It should be aged 120 days or hot composted before used.
See if there is a composting facility near you. Most of them will post their analysis or give you their compost analysis if you ask. Most compost is alkaline, but it also buffers pH and acts more neutral. Compost is something that should be added every year but it is best to add a good blended compost made from a variety of materials. That is why it is a good idea to start a compost pile before you start a garden. It will also reduce your waste because you can compost most of your clean yard and garden waste and save space at the landfill.
I would not add a lot of dolomite or wood ashes or anything that would change pH until you get a a good soil test with recommendations about what and how much to add. If your pH needs to be corrected, the test will tell you how much lime or sulfur you need to add. Nitrogen, Phosphorus excess can leach into the water table and back into lakes and oceans so you should not apply more than you need and use nutrient scavengers to clean up any excess. Excesses of phosphorus, potassium and calcium take years to fix as they have to be leached and diluted out. Any correction to pH will take six months to change anything one way or another so you don't want to over correct. Compost you added 3 years ago would not have much residual now. Calcium/Magnesium ratio does affect pH but it usually gets more alkaline if you have been adding alkaline compost. I usually just switch to peat moss instead since it stabilizes an alkaline pH faster and for a longer time than sulfur.
Your soil in your picture does not look like it has a lot of organic matter in it.
All soil tests now recommend adding organic matter. I only add about 4 inches of compost and mix it in my soil. A blended compost is better than one from a single source. Composted manures 1/2 inch. Chicken manure should not be used on an alkaline plot. It will drive the pH a half point higher. Mushroom compost is alkaline and a single source.
All soil tests will recommend nitrogen. Nitrogen is volatile and is readily lost so some nitrogen will always be recommended. However, if you have lush greens and not a lot of fruit. I would skimp on the nitrogen or plant a scavenger crop after a high user like corn without additional nitrogen to mop up any excess.
Compost is not fertilizer. Fertilize according to recommendations. Extension soil tests usually will give conventional fertilizer recommendations. You need to ask for organic. You may have to convert lbs per acre to lbs per 100 sq ft. unless your extension gives your recommendations per 100 or 1000 sq ft. The cheat conversion is One acre = 43560 sq ft. 100/43560 = approx 0.002. Multiply your lbs per acre by 0.002 = lbs per 100 sq ft. (10x10)
You have mostly heavy feeders: corn, cucumber, squash, melons
Your peas and beans are the soil builders. You don't have any root crops which would be your light feeders. Onions, beets, turnips, kale maybe something to think about. Some can tolerate a light frost. If you have 5 beds it would be ideal since you could rotate your heavy feeders with soil builders and use one bed for making compost, lasagna style. When I did compost, I found that to be the best way to rest the garden was to build the compost pile on the fallow section. After all, the best part was always on the bottom of the pile. Since you have so many heavy feeders you need to get the fertilizer right. Pests are problems when your plants are stressed. If you include plants to attract beneficial insects it is better than spraying in the long run.
https://www.co.thurston.wa.us/health/ehc ... _sglpg.pdf
https://www.ufseeds.com/Delaware-Vegetab ... endar.html
Happy gardening in Hawaii. Gardens are where people grow.